You simply should not miss the Olomouc castle site situated on the Wenceslas Hill! Right here in 1306, the last Přemyslid, the Czech king Wenceslas III, was assassinated. You can admire the Bishop's Palace with its famous Romanesque windows, the gothic St. Wenceslas Cathedral, today the seat of the Archbishop of Olomouc, or the Archdiocesan Museum founded on the initiative of Pope John Paul II.
http://tourism.olomouc.eu/sights/olomouc-castle/en